Question:
A square of perimeter 88 cm and a circle of perimeter 88 cm are given. Which figure has larger area and by how much?
A square of perimeter 88 cm and a circle of perimeter 88 cm are given. Which figure has larger area and by how much?
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When comparing areas of figures with the same perimeter, remember that a circle will always have a larger area than a square when their perimeters are equal, as the circle uses the perimeter more efficiently.
Updated On: Mar 10, 2025
- 125 cm²
- 128 cm²
- 132 cm²
- 125 cm²
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The Correct Option is C
Solution and Explanation
The perimeter of both the square and the circle is given as 88 cm.
Step 1: Calculate the area of the square
\[
\text{Side length of square} = \frac{88}{4} = 22 \, \text{cm}
\]
\[
\text{Area of square} = 22^2 = 484 \, \text{cm}^2
\]
Step 2: Calculate the area of the circle The formula for the circumference of a circle is: \[ C = 2 \pi r \] We know the circumference of the circle is 88 cm, so: \[ 88 = 2 \pi r \] \[ r = \frac{88}{2 \pi} = \frac{88}{6.28} = 14 \, \text{cm} \] Now calculate the area of the circle: \[ \text{Area of circle} = \pi r^2 = 3.1416 \times (14)^2 = 3.1416 \times 196 = 615.75 \, \text{cm}^2 \]
Step 3: Conclusion Thus, the area of the circle is larger than the area of the square by: \[ 615.75 - 484 = 132 \, \text{cm}^2 \] Final Answer: The correct answer is (c) 132 cm².
Step 2: Calculate the area of the circle The formula for the circumference of a circle is: \[ C = 2 \pi r \] We know the circumference of the circle is 88 cm, so: \[ 88 = 2 \pi r \] \[ r = \frac{88}{2 \pi} = \frac{88}{6.28} = 14 \, \text{cm} \] Now calculate the area of the circle: \[ \text{Area of circle} = \pi r^2 = 3.1416 \times (14)^2 = 3.1416 \times 196 = 615.75 \, \text{cm}^2 \]
Step 3: Conclusion Thus, the area of the circle is larger than the area of the square by: \[ 615.75 - 484 = 132 \, \text{cm}^2 \] Final Answer: The correct answer is (c) 132 cm².
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